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Exactly 71 people are standing in a single queue

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Exactly 71 people are standing in a single queue  [#permalink]

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New post 23 Feb 2018, 11:16
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Exactly 71 people are standing in a single queue outside a store on black Friday. If these 71 people also include Daniel and Maria, then how many people are standing in front of Maria in the queue?

(1) When counted from the back of the queue, Daniel is at 19th position and there are exactly 7 people between Daniel and Maria.

(2) The number of people in front of Maria in the queue are 18 more than the number of people behind Maria in the queue.
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New post 23 Feb 2018, 11:27
amanvermagmat wrote:
Exactly 71 people are standing in a single queue outside a store on black Friday. If these 71 people also include Daniel and Maria, then how many people are standing in front of Maria in the queue?

(1) When counted from the back of the queue, Daniel is at 19th position and there are exactly 7 people between Daniel and Maria.

(2) The number of people in front of Maria in the queue are 18 more than the number of people behind Maria in the queue.


Statement 1: Provides Daniel's position but we do not know whether Maria is in front or behind Daniel. In wither case number of people standing in front of Maria will be different. Hence Insufficient

Statement 2: if number of people behind Maria is \(x-18\), then number of people in front of Maria will be \(x\)

so we have \(x+x-18=70 => x=44\). Sufficient

Option B
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Exactly 71 people are standing in a single queue  [#permalink]

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New post 23 Feb 2018, 11:38
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Exactly 71 people are standing in a single queue outside a store on black Friday. If these 71 people also include Daniel
and Maria, then how many people are standing in front of Maria in the queue?

(1) When counted from the back of the queue, Daniel is at 19th position and there are exactly 7 people between Daniel and Maria.
This statement is not enough as Maria could be 7 places before/after Daniel.
We cannot arrive at a unique answer for the total number of people ahead of Maria (Insufficient)

(2) The number of people in front of Maria in the queue are 18 more than the number of people behind Maria in the queue.
It x is the position she is at from behind the queue, then 18+x+1+x = 71.
2x + 19 = 71 -> x = 26
So basically, she must be at the 45(18+26)th position in the queue (Sufficient - Option B)
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Exactly 71 people are standing in a single queue  [#permalink]

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New post 23 Feb 2018, 15:43
St 1 is not sufficient as we don't know whether Mary is in front of or behind Daniel in the queue.
St 2 is sufficient as we can set an equation using : x+18 people in front of Mary, x people behind Mary
In total there will be x+18+Mary+x = 71
2x=71-19 ,
x=26 , so there are 26+18 people are in front of Mary
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Re: Exactly 71 people are standing in a single queue  [#permalink]

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New post 27 Feb 2018, 01:16
amanvermagmat wrote:
Exactly 71 people are standing in a single queue outside a store on black Friday. If these 71 people also include Daniel and Maria, then how many people are standing in front of Maria in the queue?

(1) When counted from the back of the queue, Daniel is at 19th position and there are exactly 7 people between Daniel and Maria.

(2) The number of people in front of Maria in the queue are 18 more than the number of people behind Maria in the queue.

IMO B
statement 1 we don't know whether maria is in front or back of daniel.
statement 2 tell us exact place of maria by telling us number of people in front and back of her.
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Re: Exactly 71 people are standing in a single queue  [#permalink]

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New post 27 Feb 2018, 02:59
B.
1 states the position of Daniel, and the people between him and Maria but she may be in front of him or behind. Hence, not sufficient. BCE

2. This statement can lead to the exact location of Maria by establishing an equation between behind and front people. Hence, sufficient.


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Re: Exactly 71 people are standing in a single queue  [#permalink]

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New post 28 Feb 2018, 00:11
amanvermagmat wrote:
Exactly 71 people are standing in a single queue outside a store on black Friday. If these 71 people also include Daniel and Maria, then how many people are standing in front of Maria in the queue?

(1) When counted from the back of the queue, Daniel is at 19th position and there are exactly 7 people between Daniel and Maria.

(2) The number of people in front of Maria in the queue are 18 more than the number of people behind Maria in the queue.


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Re: Exactly 71 people are standing in a single queue   [#permalink] 28 Feb 2018, 00:11
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